The disclosure herein relates generally to microwave tomography. More particularly, the disclosure herein pertains to methods and systems of microwave tomography (MWT) for use in, e.g., imaging applications (e.g., tumor detection in human tissue, etc.).
Tomography is imaging by sections or sectioning to convey internal structures of an object, for example, the human body or the earth. Microwave tomography (MWT) systems irradiate an object of interest, or object to be imaged, with electromagnetic energy, measure or sample the resultant scattered electromagnetic energy, and generate or reconstruct an image of the object based on the resultant scattered electromagnetic energy. “Scattering” is a general physical process whereby some forms of radiation, such as light, sound, or moving particles, for example, are forced to deviate from a straight trajectory by one or more non-uniformities in a medium through which it passes. The “inverse problem” may be used to determine the characteristics of an object of interest such as its shape and internal constitution from the resultant scattered electromagnetic energy.
An exemplary tomography system, e.g., a microwave tomography system, is described in Patent Cooperation Treaty Patent Application Pub No. WO 2009/066186 A2 filed on Nov. 21, 2008 and entitled “System and Methods of Improved Tomography Imaging,” which is incorporated herein by reference in its entirety.
Contributions to MWT have been made in all aspects of the technology, especially the development of improved inversion algorithms (see, e.g., T. Rubaek, P. M. Meaney, P. Meincke, and K. D. Paulsen, “Nonlinear microwave imaging for breast-cancer screening using Gauss-Newton's method and the CGLS inversion algorithm,” IEEE Trans. Antennas Propag., vol. 55, no. 8, pp. 2320-2331, August 2007; A. Abubakar, P. M. van den Berg, and J. J. Mallorqui, “Imaging of biomedical data using a multiplicative regularized contrast source inversion method,” IEEE Trans. Microwave Theory Tech., vol. 50, no. 7, pp. 1761-1777, July 2002; J. D. Zaeytijd, A. Franchois, C. Eyraud, and J.-M. Geffrin, “Full-wave three-dimensional microwave imaging with a regularized Gauss-Newton method-theory and experiment,” IEEE Trans. Antennas Propag., vol. 55, no. 11, pp. 3279-3292, November 2007; and W. C. Chew and Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imaging, vol. 9, no. 2, pp. 218-225, 1990).
Further, diverse antenna or transducer systems have been utilized in the actual physical setups used to collect electromagnetic scattering data in MWT systems (see, e.g., P. Meaney, M. Fanning, D. Li, S. Poplack, and K. Paulsen, “A clinical prototype for active microwave imaging of the breast,” IEEE Trans. Microwave Theory Tech., vol. 48, no. 11, pp. 1841-1853, November 2000; A. Franchois, A. Joisel, C. Pichot, and J.-C. Bolomey, “Quantitative microwave imaging with a 2.45-GHz planar microwave camera,” IEEE Trans. Med. Imag., vol. 17, no. 4, pp. 550-561, August 1998; A. Broquetas, J. Romeu, J. Rius, A. Elias-Fuste, A. Cardama, and L. Jofre, “Cylindrical geometry: a further step in active microwave tomography,” IEEE Trans. Microwave Theory Tech., vol. 39, no. 5, pp. 836-844, May 1991; S. Y. Semenov, R. H. Svenson, A. E. Bulyshev, A. E. Souvorov, A. G. Nazarov, Y. E. Sizov, V. G. Posukh, A. Pavlovsky, P. N. Repin, A. N. Starostin, B. A. Voinov, M. Taran, G. P. Tastis, and V. Y. Baranov, “Three-dimensional microwave tomography: Initial experimental imaging of animals,” IEEE Trans. Biomed. Eng., vol. 49, no. 1, pp. 55-63, January 2002; A. Fhager, P. Hashemzadeh, and M. Persson, “Reconstruction quality and spectral content of an electromagnetic time-domain inversion algorithm,” IEEE Trans. Biomed. Eng., vol. 53, no. 8, pp. 1594-1604, August 2006; C. Yu, M. Yuan, J. Stang, E. Bresslour, R. George, G. Ybarra, W. Joines, and Q. H. Liu, “Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data,” IEEE Trans. Microwave Theory Tech., vol. 56, no. 4, pp. 991-1000, April 2008; T. Rubaek, O. Kim, and P. Meincke, “Computational validation of a 3D microwave imaging system for breast-cancer screening,” IEEE Trans. Antennas Propag., vol. 57, no. 7, pp. 2105-2115, July 2009; and A. E. Bulyshev, A. E. Souvorov, S. Y. Semenov, R. H. Svenson, A. G. Nazarov, Y. E. Sizov, and G. P. Tastis, “Three dimensional microwave tomography theory and computer experiments in scalar approximation,” Inverse Probl., vol. 16, pp. 863-875, 2000).
In many previous MWT systems, the object of interest and the antennas are contained within a chamber, usually made from a dielectric material, such as plexiglass. The dielectric chamber is usually filled with a lossy matching fluid, e.g., a 87:13 glycerin:water solution (see, e.g., T. Rubaek, P. M. Meaney, P. Meincke, and K. D. Paulsen, “Nonlinear microwave imaging for breast-cancer screening using Gauss-Newton's method and the CGLS inversion algorithm,” IEEE Trans. Antennas Propag., vol. 55, no. 8, pp. 2320-2331, August 2007; and P. M. Meaney, M. W. Fanning, T. Raynolds, C. J. Fox., Q. Fang, C. A. Kogel, S. P. Poplack, and K. D. Paulsen, “Initial clinical experience with microwave breast imaging in women with normal mammography,” Acad Radiol., March 2007).
Further, in one or more previous MWT systems, the object of interest and the antennas have been enclosed by a circular metallic enclosure (see, e.g., L. Crocco and A. Litman, “On embedded microwave imaging systems: retrievable information and design guidelines,” Inverse Problems, vol. 25, no. 6, 2009, 065001 (17 pp); C. Gilmore and J. LoVetri, “Enhancement of microwave tomography through the use of electrically conducting enclosures,” Inverse Problems, vol. 24, no. 3, 2008, 035008 (21 pp); A. Franchois and A. G. Tijhuis, “A quasi-Newton reconstruction algorithm for a complex microwave imaging scanner environment,” Radio Sci., vol. 38, no. 2, 2003; R. Lencrerot, A. Litman, H. Tortel, and J.-M. Geffrin, “Measurement strategies for a confined microwave circular scanner,” Inverse Problems in Science and Engineering, pp. 1-16, January 2009; “Imposing Zernike representation for imaging two-dimensional targets,” Inverse Problems, vol. 25, no. 3, 2009, 035012 (21 pp); and P. Mojabi and J. LoVetri, “Eigenfunction contrast source inversion for circular metallic enclosures,” Inverse Problems, vol. 26, no. 2, February 2010, 025010 (23 pp)). Still further, in previous MWT systems, the object of interest and the antennas have been enclosed in conducting cylinders of arbitrary shapes (see, e.g., P. Mojabi, C. Gilmore, A. Zakaria, and J. LoVetri, “Biomedical microwave inversion in conducting cylinders of arbitrary shapes,” in 13th International Symposium on Antenna Technology and Applied Electromagnetics and the Canadian Radio Science Meeting (ANTEM/URSI), February 2009, pp. 1-4).
Obtaining quality images using MWT may require accurate collection of a substantial amount of electromagnetic scattering data, which may often be performed using a relatively large number of co-resident antennas. For example, many present MWT systems include antenna arrays that range from 16 to 32 elements in which small monopoles or Vivaldi antennas have been used. These large antenna arrays may facilitate gathering of bistatic scattering data at many angles without mechanically repositioning the antennas. The antenna elements themselves are not typically taken fully into account in the electromagnetic system model of the associated nonlinear optimization problem, although it may be a consideration in achieving good images (compare, e.g., the antenna compensation schemes in the following: K. Paulsen and P. Meaney, “Nonactive antenna compensation for fixed-array microwave imaging. I. Model development,” IEEE Trans. Med. Imag., vol. 18, no. 6, pp. 496-507, June 1999; P. Meaney, K. Paulsen, J. Chang, M. Fanning, and A. Hartov, “Nonactive antenna compensation for fixed-array microwave imaging. II. Imaging results,” IEEE Trans. Med. Imag., vol. 18, no. 6, pp. 508-518, June 1999; and O. Franza, N. Joachimowicz, and J.-C. Bolomey, “SICS: A sensor interaction compensation scheme for microwave imaging,” IEEE Trans. Antennas Propag., vol. 50, no. 2, pp. 211-216, February 2002).
Including the antennas in the MWT system model may be one way of reducing modeling error that exists between a numerical system model, used in an inversion algorithm, and the actual system, from which data is collected. Modeling error may also occur when assuming a homogeneous unbounded domain for the numerical system model (i.e., assuming that the matching fluid extends to infinity) because the boundary conditions for the dielectric discontinuity, e.g., at a MWT system's dielectric casing (e.g., a plexiglass casing), may actually be required to properly account for the finite extent of the matching-fluid region. Both the antenna and the boundary condition modeling errors may be reduced by using lossy matching fluid of sufficiently high loss such that electromagnetic energy returning from the boundary, or any passive antenna, to any receiving antenna is not appreciable. Although the use of a lossy matching fluid may reduce modeling errors, the net effect of using a lossy matching fluid in MWT systems may also be to reduce the accuracy of the complex permittivity profile reconstructions because the addition of any loss reduces the dynamic range and achievable signal-to-noise ratio of the system.
A MWT system that uses a rotating metallic hexagonal-shaped container where the object of interest is illuminated by waveguides (e.g., each of the waveguides acts as both a transmitter and a receiver) connected, or fixedly attached, to each side of the metallic container has been previously described (see, e.g., E. Wadbro and M. Berggren, “Microwave tomography using topology optimization techniques,” SIAM J. Sci. Comput., vol. 30, no. 3, pp. 1613-1633, 2008). In this system, a container, along with the attached waveguides, may be rotated about the object of interest to collect additional scattering data, and topology optimization techniques may be used to invert the data. At each rotation, however, this system produces an identical incident field with respect to the boundary (i.e., the boundary condition) of the enclosure because the microwave sources (i.e., the waveguides) remain fixed with respect to the boundary. In other words, this system produces identical boundary conditions with respect to its waveguides (i.e., its transmitters and receivers) because the waveguides are fixedly attached to the enclosure, and therefore, rotate with the enclosure.